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Erschienen in:
2014 | OriginalPaper | Buchkapitel
A Finite Difference Method for Electrostatics with Curved Boundaries
verfasst von : David Edwards
Erschienen in: Transactions on Engineering Technologies
Verlag: Springer Netherlands
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Abstract
Difficulties of the finite difference method occur when a boundary does not lie on the mesh points in the overlaid meshpoint array but passes between them. To overcome this limitation and at the same time to effect high precision solutions to the curvilinear problem a solution is described which extends the internal space of the geometry to the other side of the enclosing boundary by analytic continuation. The boundary potential itself is incorporated into the values of near mesh points by interpolation from the boundary. Using this technique precisions of the order of \(\sim \!10^{-13}\) have been obtained for the concentric sphere geometry. Thus a fundamental limitation of the finite difference method has been removed.